It is useful to remember the consequences of these expressions for the shape of the LDOS at and around a vortex core[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The electron and hole LDOS follows approximately the sum over all \(\vert \psi _n^+(\mathbf {r})\vert ^2\)  and \(\vert \psi _n^-(\mathbf {r})\vert ^2\) , respectively, convoluted with the Fermi function (which is shifted from the Fermi level by \(eV\)  in presence of a bias voltage \(V\) ). The difference between electron and hole LDOS occurs at the rapid atomic scale oscillation \(k_Fr\) , because of the phase shift induced by \(\eta _n\) . This difference is however washed out in the experiment because \(k_BT\gg (E_{n}-E_{n-1})\approx \frac{\Delta _0^2}{E_F}\)  in 2H-NbSe\(_2\) , 2H-NbSe\(_{1.8}\) S\(_{0.2}\)  and in many other superconductors. As a result, the LDOS shows a electron-hole symmetric patterns.
